The topological analysis of electronic charge densities: A reassessment of foundations

In this account the relationship between the topological analysis of electronic charge densities and the general theory of dynamical systems is considered in detail. It is shown that the main theorems of structural stability are best appreciated within the context of the general theory of dynamical systems. On the other hand, it is demonstrated that this theory may set the stage for a generalized topological analysis. This general framework could be applied easily to various scalar functions. In the end, it is emphasized that the very concepts of structure and structural stability are not intrinsically tied to the nuclear coordinates. Accordingly, by employing new variables like temperature or pressure it is possible to construct novel control spaces.